Definition of the Subject
Although analog computation was eclipsed by digital computation in the second half of the twentieth century, it is returning as an importantalternative computing technology. Indeed, as explained in this article, theoretical results imply that analog computation can escape from the limitationsof digital computation. Furthermore, analog computation has emerged as an important theoretical framework for discussing computation in the brain andother natural systems.
Analog computation gets its name from an analogy, orsystematic relationship, between the physical processes in the computer and those in thesystem it is intended to model or simulate (the primarysystem). For example, the electrical quantities voltage, current, and conductancemight be used as analogs of the fluid pressure, flow rate, and pipe diameter. Morespecifically, in traditional analog computation, physical quantities in the computation obeythe same mathematical laws as physical quantities in the...
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsAbbreviations
- Accuracy:
-
The closeness of a computation to the corresponding primary system.
- BSS:
-
The theory of computation over the real numbers defined by Blum, Shub, and Smale.
- Church–Turing (CT) computation:
-
The model of computation based on the Turing machine and other equivalent abstract computing machines; commonly accepted as defining the limits of digital computation.
- EAC:
-
Extended analog computer defined by Rubel.
- GPAC:
-
General-purpose analog computer.
- Nomograph:
-
A device for the graphical solution of equations by means of a family of curves and a straightedge.
- ODE:
-
Ordinary differential equation.
- PDE:
-
Partial differential equation.
- Potentiometer:
-
A variable resistance, adjustable by the computer operator, used in electronic analog computing as an attenuator for setting constants and parameters in a computation.
- Precision:
-
The quality of an analog representation or computation, which depends on both resolution and stability.
- Primary system:
-
The system being simulated, modeled, analyzed, or controlled by an analog computer, also called the target system.
- Scaling:
-
The adjustment, by constant multiplication, of variables in the primary system (including time) so that the corresponding variables in the analog systems are in an appropriate range.
- TM:
-
Turing machine.
Bibliography
Primary Literature
Anderson JA (1995) An Introduction to Neural Networks. MIT Press, Cambridge
Ashley JR (1963) Introduction to Analog Computing. Wiley, New York
Aspray W (1993) Edwin L. Harder and the Anacom: Analog computing at Westinghouse. IEEE Ann Hist of Comput 15(2):35–52
Ben-Hur A, Siegelmann HT, Fishman S (2002) A theory of complexity for continuous time systems. J Complex 18:51–86
Bissell CC (2004) A great disappearing act: The electronic analogue computer. In: IEEE Conference on the History of Electronics, Bletchley, June 2004. pp 28–30
Blum L, Cucker F, Shub M, Smale S (1998) Complexity and Real Computation. Springer, Berlin
Blum L, Shub M, Smale S (1988) On a theory of computation and complexity over the real numbers: NP completeness, recursive functions and universal machines. Bulletin Am Math Soc 21:1–46
Bournez O, Campagnolo ML, Graça DS, Hainry E. The General Purpose Analog Computer and computable analysis are two equivalent paradigms of analog computation. In: Theory and Applications of Models of Computation (TAMC 2006). Lectures Notes in Computer Science, vol 3959. Springer, Berlin, pp 631–643
Bournez O, Cosnard M (1996) On the computational power of dynamical systems and hybrid systems. Theor Comput Sci 168(2):417–59
Bowles MD (1996) US technological enthusiasm and British technological skepticism in the age of the analog brain. Ann Hist Comput 18(4):5–15
Branicky MS (1994) Analog computation with continuous ODEs. In: Proceedings IEEE Workshop on Physics and Computation, Dallas, pp 265–274
Brockett RW (1988) Dynamical systems that sort lists, diagonalize matrices and solve linear programming problems. In: Proceedings 27th IEEE Conference Decision and Control, Austin, December 1988, pp 799–803
Camazine S, Deneubourg J-L, Franks NR, Sneyd G, Theraulaz J, Bonabeau E (2001) Self-organization in Biological Systems. Princeton Univ. Press, New York
Changeux J-P (1985) Neuronal Man: The Biology of Mind (trans: Garey LL). Oxford University Press, Oxford
Clymer AB (1993) The mechanical analog computers of Hannibal Ford and William Newell. IEEE Ann Hist Comput 15(2):19–34
Davidson EH (2006) The Regulatory Genome: Gene Regulatory Networks in Development and Evolution. Academic Press, Amsterdam
Davies JA (2005) Mechanisms of Morphogensis. Elsevier, Amsterdam
Davis M (2004) The myth of hypercomputation. In: Teuscher C (ed) Alan Turing: Life and Legacy of a Great Thinker. Springer, Berlin, pp 195–212
Davis M (2006) Why there is no such discipline as hypercomputation. Appl Math Comput 178:4–7
Fakhraie SM, Smith KC (1997) VLSI-Compatible Implementation for Artificial Neural Networks. Kluwer, Boston
Franklin S, Garzon M (1990) Neural computability. In: Omidvar OM (ed) Progress in Neural Networks, vol 1. Ablex, Norwood, pp 127–145
Freeth T, Bitsakis Y, Moussas X, Seiradakis JH, Tselikas A, Mangou H, Zafeiropoulou M, Hadland R, Bate D, Ramsey A, Allen M, Crawley A, Hockley P, Malzbender T, Gelb D, Ambrisco W, Edmunds MG (2006) Decoding the ancient Greek astronomical calculator known as the Antikythera mechanism. Nature 444:587–591
Garzon M, Franklin S (1989) Neural computability ii (extended abstract). In: Proceedings, IJCNN International Joint Conference on Neural Networks, vol 1. Institute of Electrical and Electronic Engineers, New York, pp 631–637
Garzon M, Franklin S (1990) Computation on graphs. In: Omidvar OM (ed) Progress in Neural Networks, vol 2. Ablex, Norwood
Goldstine HH (1972) The Computer from Pascal to von Neumann. Princeton, Princeton
Grossberg S (1967) Nonlinear difference-differential equations in prediction and learning theory. Proc Nat Acad Sci USA 58(4):1329–1334
Grossberg S (1973) Contour enhancement, short term memory, and constancies in reverberating neural networks. Stud Appl Math LII:213–257
Grossberg S (1976) Adaptive pattern classification and universal recoding: I. parallel development and coding of neural feature detectors. Biol Cybern 23:121–134
Hartl DL (1994) Genetics, 3rd edn. Jones & Bartlett, Boston
Hopfield JJ (1984) Neurons with graded response have collective computational properties like those of two-state neurons. Proc Nat Acad Sci USA 81:3088–92
Howe RM (1961) Design Fundamentals of Analog Computer Components. Van Nostrand, Princeton
Khatib O (1986) Real-time obstacle avoidance for manipulators and mobile robots. Int J Robot Res 5:90–99
Kirchhoff G (1845) Ueber den Durchgang eines elektrischen Stromes durch eine Ebene, insbesondere durch eine kreisförmige. Ann Phys Chem 140(64)(4):497–514
Lang GF (2000) Analog was not a computer trademark! Why would anyone write about analog computers in year 2000? Sound Vib 34(8):16–24
Lipshitz L, Rubel LA (1987) A differentially algebraic replacment theorem. Proc Am Math Soc 99(2):367–72
Maass W, Sontag ED (1999) Analog neural nets with Gaussian or other common noise distributions cannot recognize arbitrary regular languages. Neural Comput 11(3):771–782
MacLennan BJ (1987) Technology-independent design of neurocomputers: The universal field computer. In: Caudill M, Butler C (eds) Proceedings of the IEEE First International Conference on Neural Networks, vol 3, IEEE Press, pp 39–49
MacLennan BJ (1990) Field computation: A theoretical framework for massively parallel analog computation, parts I–IV. Technical Report CS-90-100, Department of Computer Science, University of Tennessee, Knoxville. Available from http://www.cs.utk.edu/%7Emclennan. Accessed 20 May 2008
MacLennan BJ (1991) Gabor representations of spatiotemporal visual images. Technical Report CS-91-144, Department of Computer Science, University of Tennessee, Knoxville. Available from http://www.cs.utk.edu/%7Emclennan. Accessed 20 May 2008
MacLennan BJ (1994) Continuous computation and the emergence of the discrete. In: Pribram KH (ed) Origins: Brain & Self-Organization, Lawrence Erlbaum, Hillsdale, pp 121–151.
MacLennan BJ (1994) “Words lie in our way”. Minds Mach 4(4):421–437
MacLennan BJ (1995) Continuous formal systems: A unifying model in language and cognition. In: Proceedings of the IEEE Workshop on Architectures for Semiotic Modeling and Situation Analysis in Large Complex Systems, Monterey, August 1995. pp 161–172. Also available from http://www.cs.utk.edu/%7Emclennan. Accessed 20 May 2008
MacLennan BJ (1999) Field computation in natural and artificial intelligence. Inf Sci 119:73–89
MacLennan BJ (2001) Can differential equations compute? Technical Report UT-CS-01-459, Department of Computer Science, University of Tennessee, Knoxville. Available from http://www.cs.utk.edu/%7Emclennan. Accessed 20 May 2008
MacLennan BJ (2003) Transcending Turing computability. Minds Mach 13:3–22
MacLennan BJ (2004) Natural computation and non-Turing models of computation. Theor Comput Sci 317:115–145
MacLennan BJ (in press) Super-Turing or non-Turing? Extending the concept of computation. Int J Unconv Comput, in press
Maini PK, Othmer HG (eds) (2001) Mathematical Models for Biological Pattern Formation. Springer, New York
Maziarz EA, Greenwood T (1968) Greek Mathematical Philosophy. Frederick Ungar, New York
McClelland JL, Rumelhart DE, the PDP Research Group. Parallel Distributed Processing: Explorations in the Microstructure of Cognition, vol 2: Psychological and Biological Models. MIT Press, Cambridge
Mead C (1987) Silicon models of neural computation. In: Caudill M, Butler C (eds) Proceedings, IEEE First International Conference on Neural Networks, vol I. IEEE Press, Piscataway, pp 91–106
Mead C (1989) Analog VLSI and Neural Systems. Addison-Wesley, Reading
Mills JW (1996) The continuous retina: Image processing with a single-sensor artificial neural field network. In: Proceedings IEEE Conference on Neural Networks. IEEE Press, Piscataway
Mills JW, Himebaugh B, Kopecky B, Parker M, Shue C, Weilemann C (2006) “Empty space” computes: The evolution of an unconventional supercomputer. In: Proceedings of the 3rd Conference on Computing Frontiers, New York, May 2006. ACM Press, pp 115–126
Moore C (1996) Recursion theory on the reals and continuous-time computation. Theor Comput Sci 162:23–44
Moore GE (1965) Cramming more components onto integrated circuits. Electronics 38(8):114–117
Murray JD (1977) Lectures on Nonlinear Differential-Equation Models in Biology. Oxford, Oxford
Omohundro S (1984) Modeling cellular automata with partial differential equations. Physica D 10:128–34, 1984.
Orponen P (1997) A survey of continous-time computation theory. In: Advances in Algorithms, Languages, and Complexity, Kluwer, Dordrecht, pp 209–224
Orponen P, Matamala M (1996) Universal computation by finite two-dimensional coupled map lattices. In: Proceedings, Physics and Computation 1996, New England Complex Systems Institute, Cambridge, pp 243–7
Owens L (1986) Vannevar Bush and the differential analyzer: The text and context of an early computer. Technol Culture 27(1):63–95
Peterson GR (1967) Basic Analog Computation. Macmillan, New York
Pour-El MB (1974) Abstract computability and its relation to the general purpose analog computer (some connections between logic, differential equations and analog computers). Trans Am Math Soc 199:1–29
Pour-El MB, Richards I (1979) A computable ordinary differential equation which possesses no computable solution. Ann Math Log 17:61–90
Pour-EL MB, Richards I (1981) The wave equation with computable initial data such that its unique solution is not computable. Adv Math 39:215–239
Pour-El MB, Richards I (1982) Noncomputability in models of physical phenomena. Int J Theor Phys, 21:553–555
Puchta S (1996) On the role of mathematics and mathematical knowledge in the invention of Vannevar Bush's early analog computers. IEEE Ann Hist Comput 18(4):49–59
Reiner JM (1968) The Organism as an Adaptive Control System. Prentice-Hall, Englewood Cliffs
Rimon E, Koditschek DE (1989) The construction of analytic diffeomorphisms for exact robot navigation on star worlds. In: Proceedings of the 1989 IEEE International Conference on Robotics and Automation, Scottsdale AZ. IEEE Press, New York, pp 21–26
Rogers AE, Connolly TW (1960) Analog Computation in Engineering Design. McGraw-Hill, New York
Rubel LA (1985) The brain as an analog computer. J Theor Neurobiol 4:73–81
Rubel LA (1988) Some mathematical limitations of the general-purpose analog computer. Adv Appl Math 9:22–34
Rubel LA (1993) The extended analog computer. Adv Appl Math 14:39–50
Rumelhart DE, McClelland JL, the PDP Research Group (1986) Parallel Distributed Processing: Explorations in the Microstructure of Cognition, vol 1: Foundations. MIT Press, Cambridge
Sanger TD (1996) Probability density estimation for the interpretation of neural population codes. J Neurophysiol 76:2790–2793
Shannon CE (1941) Mathematical theory of the differential analyzer. J Math Phys Mass Inst Technol 20:337–354
Shannon CE (1993) Mathematical theory of the differential analyzer. In: Sloane NJA, Wyner AD (eds) Claude Elwood Shannon: Collected Papers. IEEE Press, New York, pp 496–513
Siegelmann HT (1999) Neural Networks and Analog Computation: Beyond the Turing Limit. Birkhäuser, Boston
Siegelmann HT, Ben-Hur A, Fishman S (1999) Computational complexity for continuous time dynamics. Phys Rev Lett 83(7):1463–6
Siegelmann HT, Sontag ED (1994) Analog computation via neural networks. Theor Comput Sci 131:331–360
Small JS (1993) General-purpose electronic analog computing. IEEE Ann Hist Comput 15(2):8–18
Small JS (2001) The Analogue Alternative: The electronic analogue computer in Britain and the USA, 1930–1975. Routledge, London & New York
Stannett M (19901) X-machines and the halting problem: Building a super-Turing machine. Form Asp Comput 2:331–341
Thomson W (Lord Kelvin) (1876) Mechanical integration of the general linear differential equation of any order with variable coefficients. Proc Royal Soc 24:271–275
Thomson W (Lord Kelvin) (1878) Harmonic analyzer. Proc Royal Soc 27:371–373
Thomson W (Lord Kelvin) (1938). The tides. In: The Harvard Classics, vol 30: Scientific Papers. Collier, New York, pp 274–307
Truitt TD, Rogers AE (1960) Basics of Analog Computers. John F. Rider, New York
van Gelder T (1997) Dynamics and cognition. In: Haugeland J (ed) Mind Design II: Philosophy, Psychology and Artificial Intelligence. MIT Press, Cambridge MA, revised & enlarged edition, Chap 16, pp 421–450
Weyrick RC (1969) Fundamentals of Analog Computers. Prentice-Hall, Englewood Cliffs
Wolpert DH (1991) A computationally universal field computer which is purely linear. Technical Report LA-UR-91-2937. Los Alamos National Laboratory, Loa Alamos
Wolpert DH, MacLennan BJ (1993) A computationally universal field computer that is purely linear. Technical Report CS-93-206. Dept. of Computer Science, University of Tennessee, Knoxville
Books and Reviews
Fifer S (1961) Analog computation: Theory, techniques and applications, 4 vols. McGraw-Hill, New York
Bissell CC (2004) A great disappearing act: The electronic analogue computer. In: IEEE conference on the history of electronics, 28–30 Bletchley, June 2004
Lipka J (1918) Graphical and mechanical computation. Wiley, New York
Mead C (1989) Analog VLSI and neural systems. Addison-Wesley, Reading
Siegelmann HT (1999) Neural networks and analog computation: Beyond the Turing limit. Birkhäuser, Boston
Small JS (2001) The analogue alternative: The electronic analogue computer in Britain and the USA, 1930–1975. Routledge, London & New York
Small JS (1993) General-purpose electronic analog computing: 1945–1965. IEEE Ann Hist Comput 15(2):8–18
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag
About this entry
Cite this entry
MacLennan, B.J. (2009). Analog Computation. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, New York, NY. https://doi.org/10.1007/978-0-387-30440-3_19
Download citation
DOI: https://doi.org/10.1007/978-0-387-30440-3_19
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-75888-6
Online ISBN: 978-0-387-30440-3
eBook Packages: Physics and AstronomyReference Module Physical and Materials ScienceReference Module Chemistry, Materials and Physics